Selmer's curve $3X^3+4y^3+5z^3=0$ is an examplea non-example (see the comment below) but somwhat relevant. See Theorem 1 in Mazur's article titled ON THE PASSAGE FROM LOCAL TO GLOBAL IN NUMBER THEORY. I don't know how he obtains the equations of the companions. I hope someone can explain this.
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Selmer's curve $3X^3+4y^3+5z^3=0$ is an example. See Theorem 1 in Mazur's article titled ON THE PASSAGE FROM LOCAL TO GLOBAL IN NUMBER THEORY. I don't know how he obtains the equations of the companions. I hope someone can explain this. |
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